Development of Conceptual Understanding of Physical and Chemical Changes at the Macroscopic, Submicroscopic and Symbolic Level: A Cross-Age Study

In order to explain the development of understanding of chemical concepts at the macroscopic, submicroscopic and symbolic level over time, models of the expanding triangle and rising iceberg are proposed. In order to validate the two models, this study examined whether the depth of understanding of the concepts physical and chemical changes at each of the levels significantly changes with the age of students, whether selected age groups exhibit significant differences in understanding at the three levels, and whether findings for these age groups differ. Therefore, 121 14-year-old, 108 16-year-old and 112 19-year-old students completed the test that checked their understanding of the aforementioned concepts, at all three levels. The 16-and 19-year-old students significantly outperformed the 14-year-old students at each of the levels, while all age groups showed significantly better understanding of physical and chemical changes at the macroscopic and symbolic, in comparison to the submicroscopic level. It was concluded that, while the proposed models are generally valid, the applied teaching approaches and the composition of the chemistry curriculum have a profound impact on the development of students’ conceptual understanding, at all three levels of chemistry knowledge.


Introduction
Students often perceive Chemistry as an abstract and conceptually difficult subject (Childs & Sheehan, 2009), which could be related to its intrinsic nature, i. e., the fact that chemistry knowledge exists at three distinct levels (Johnstone, 2000). The macroscopic level refers to what can be seen, touched and smelt, the submicroscopic level refers to atoms, molecules, ions and structures, while the symbolic level refers to the representational use of symbols, formulae, equations, molarity, mathematical manipulation and graphs. Since none of the three levels is superior to another, but complements one another, ensuring that students understand the role of each level and relate one level to another is an important aspect of generating understandable explanations (Treagust et al., 2003). In order to achieve this goal, while learning about new chemical concepts, students are commonly required to apply multilevel thinking. Johnstone (1991) illustrated this point with a triangle with apices labeled macro, submicro and symbolic, explaining that instead of being focused on one apex, or along one side of the triangle, Chemistry teaching is predominantly conducted inside the triangle, where students must cope with all three levels at once. Research has shown that when Chemistry is taught in such a way, learners are able to develop conceptual understanding of key chemical phenomena (Ainsworth, 2006). With this in mind, Johnstone (2000), however, questioned the logic of simultaneous introduction of all three levels to novice students. His key concern was that dealing with such an amount of new information exceeds the capacity of working memory of the human brain, which restricts the number of "chunks" of new information that can be manipulated at any given time (Miller, 1968). Although working memory does not develop more slots as learners mature, familiarity with conceptual material allows each slot to hold more information (Baddeley, 1990). This ensures that the depth of understanding of any given chemical concept, at all three levels of chemistry knowledge, grows over time (Taber, 2013). But given that the macroscopic level is the most familiar to novice students, Johnstone (2000) proposed that introductory Chemistry teaching should start from this level, which should be followed by the gradual introduction of the other two levels.
In accordance with these views, Chittleborough (2014) proposed two models in order to explain the development of students' understanding of chemical concepts at the three levels of chemistry knowledge over time, both of which refer to the Johnstone's triangle. Since most Chemistry curricula are spiral, after the initial introduction to the key chemical concepts, students go on to revisit them several times during their further schooling. Consequently, students' understanding at each corner of the triangle grows, as the learning proceeds. This causes the triangle to expand, which is why the first model is named the expanding triangle model. The second proposed model, entitled the rising iceberg model, emphasizes the sequence of use of the three levels in Chemistry teaching and its influence on the development of students' conceptual understanding. The model is founded on the triangle in which the macroscopic level is presented by the top apex, while the submicroscopic and symbolic levels are presented by the bottom two apices. A horizontal line, representing the sea level, is drawn across the triangle. The area above it is shaded and it represents the students' growing understanding. Since the macroscopic level is the most appropriate for novice students, the top apex of the triangle is always included in the teaching process, while the submicroscopic and symbolic level are only introduced when needed. Over time, more and more of these two levels can be exposed to students and, consequently, the depth of their understanding grows. In analogy to this, the horizontal line moves downward and the shaded area expands.
Evidently, the two models could represent a valuable source of information about the development of students' conceptual understanding at the three levels of chemistry knowledge. However, so far, none of the models have been validated by the results of quantitative research.

Review of literature on students' understanding of physical and chemical changes at the macroscopic, submicroscopic and symbolic level
Given that physical and chemical changes represent core chemical concepts, a vast amount of research explored students' understanding of these concepts, at the three levels of chemistry knowledge.
When it comes to the changes of the states of matter, as examples of physical changes, Rahayo and Kita (2010) investigated 15-18 years old students' sound understanding of the changes from solid to liquid, solid to gaseous and liquid to gaseous state, defining sound understanding as understanding at both the macroscopic and submicroscopic level. The greatest difficulties were found relating to the change from solid to gaseous state, as less than 25 % of the students from all selected age groups showed sound understanding of the process of naphthalene sublimation. At the same time, all students demonstrated better understanding of the three types of changes at the macroscopic, in comparison to the submicroscopic level. Students' difficulties with understanding the changes of the states of matter at the submicroscopic level have also been reported by other researchers. For example, it was noted that students aged 12-13 years struggle with understanding of the change from liquid to gaseous state at this level (Nuić & Glažar, 2015). Johnson (1998aJohnson ( , 1998b found that students aged 11-14 years encounter greater difficulties with understanding the processes of evaporation and condensation in comparison to the processes of melting and freezing at the particulate level and, consequently, concluded that changes involving the gaseous state are more problematic for students. When it comes to chemical changes, Jaber and BouJaoude (2011) concluded that the 15-year-old students' understanding of chemical reactions is usually limited to the macroscopic and symbolic level, while they confound the submicroscopic level with the macroscopic level in terms of constructs and language. A tendency of the 15-year-old students to extrapolate the bulk macroscopic properties of matter to the submicroscopic level when dealing with chemical reactions was confirmed by Chandrasegaran et al. (2007), given that the students, among other things, expressed belief that reddish-brown atoms of copper were produced in the displacement reaction between zinc and copper(II) sulfate. Furthermore, the ability to represent a chemical reaction at the symbolic level proved to be no guarantee of the ability to represent the given reaction at the submicroscopic level. For example, it was ascertained that while 65.3 % of high-school students were able to correctly represent the combustion of methane at the symbolic level, only 31.1 % drew representations of this reaction that showed appropriate understanding at the particulate level (Kern et al., 2010). It was concluded that while many students appear to master the symbolic skills necessary for correct representation of chemical reactions, they often do so by treating equations as mathematical puzzles in which the numbers on the two sides of the equation have to equal each other (Krajcik, 1991).
Previous research also reported students' difficulties with distinguishing between physical and chemical changes, at both the particulate and macroscopic level. For example, more than 65 % of students aged 16-17 years expressed belief that the submicroscopic diagram which depicts splitting one molecule of a diatomic element into two atoms of that element represents a physical change, in analogy to a piece of paper being torn to two pieces (Sunyono & Sudjarwo, 2018). When it comes to the macroscopic level, it was found that around 70 % of the 14-year-old and over 50 % of the 16-year-old students thought that diluting a strong fruit juice drink by adding water was a chemical change, while 48 % of the 14-year-old and 55 % of the 16-yearold students thought that dissolving sugar in water represents a chemical change (Schollum, 1981). It was concluded that students often make the erroneous conclusion that a physical change is, in fact, a chemical change on the basis of visual cues such as "the substance changes in color, mass and state, so it would appear to be obvious that a chemical change has taken place" (Briggs & Holding, 1986, p. 63).

Research aims
As can be seen from the literature review, no previous research examined how the depth of understanding of physical and chemical changes, at each of the three levels of chemistry knowledge, changes with the age of students/number of years of chemistry learning. Furthermore, no previous research even dealt with students' understanding of physical changes at the symbolic level. In the previous two instances, it was examined whether students of one particular age group exhibit differences in the depth of understanding of chemical changes at the macroscopic, submicroscopic and symbolic level, but no previous research referring to either physical or chemical changes examined whether these differences exist when it comes to other age groups of students or whether the findings for different age groups differ. Therefore, there is a need for research findings that could be used in order to assess and validate the previously proposed models of the expanding triangle and rising iceberg, thus providing important information about the ways in which the students' conceptual understanding of physical and chemical changes at the three levels of chemistry knowledge develops over time. Consequently, the first aim of this research was to compare the depth of conceptual understanding of physical and chemical changes, at each of the three levels of chemistry knowledge, for three selected age groups of students (the 14-yearold, 16-year-old and 19-year-old students). The second aim was to ascertain whether each of the selected age groups exhibits differences in understanding of physical and chemical changes at the macroscopic, submicroscopic and symbolic level and whether the findings for the three age groups differ among them.

Research sample
The research sample consisted of 121 elementary school students aged 14 (median age = 169 months), 108 grammar school students aged 16 (median age = 193 months) and 112 grammar school students aged 19 (median age = 228 months) from Serbia. All students voluntarily accepted to participate in the study. At the time when it was conducted, the 14-year-old students were at the end of the seventh grade of elementary school and their first year of Chemistry learning, the 16-year-old students were at the end of the first year of grammar school and their third year of Chemistry learning, while the 19-year-old students were at the end of the fourth (final) year of grammar school and their sixth year of Chemistry learning. All grammar school students attended the natural sciences stream of study.
It should be noted that Chemistry curriculum in Serbia is spiral and that Chemistry is taught as a separate subject throughout both elementary and grammar school. Students are first introduced to the concepts of physical and chemical changes in the seventh grade of elementary school and they go on to revisit them in the first year of grammar school. The second year of grammar school is devoted to the study of inorganic chemistry, while the third and fourth year are devoted to the study of organic chemistry and biochemistry, respectively. Within the elaboration of all classes of organic, biochemical and inorganic compounds, students are able to acquire extensive knowledge about their physical and chemical properties and changes.

Data collection
The quantitative data were collected by means of the Achievement test, which was composed specifically for the purposes of this study. The test consisted of two main items and students were given 45 minutes to complete it. Item 1 (I1) checked students' understanding of the sublimation of water, as an example of a physical change, while Item 2 (I2) checked their understanding of the reaction of magnesium oxidation, as an example of a chemical change. Both items consisted of three subitems (one subitem for each level of chemistry knowledge).
Difficulty indices for the six subitems within the Achievement test ranged from 0.32 to 0.61 for the 14-year-old students, from 0.49 to 0.75 for the 16-year-old students and from 0.61 to 0.79 for the 19-year-old students. Discrimination indices ranged from 0.35 to 0.68 for the 14-year-old students, from 0.42 to 0.66 for the 16-year-old students and from 0.39 to 0.71 for the 19-year-old students. Since all the values of the difficulty and discrimination indices are within the acceptable range of 0.3-0.8 (Peterson et al., 1989), it was concluded that the level of difficulty and the discrimination power of the Achievement test are satisfactory. Furthermore, Cronbach's alpha was used as a measure of the test reliability and its value was 0.76 for the test completed by the 14-year-old students, 0.74 for the test completed by the 16-year-old students and 0.78 for the test completed by the 19-year-old students. Given that all the values are above the lowest acceptable value of 0.70 (Cronbach, 1951), it was concluded that the test is reliable.
Full contents of the two items in the Achievement test are presented in Figure 1 and Figure 2. 11a) select the correct symbolic representation of the sublimation of water:

Data analysis
For each of the subitems within I1 and I2, the proportion of correct answers for all three age groups of students was determined.
Normality of distribution of the 14-year-old, 16-year-old and 19-year-old students' results on the Achievement test was confirmed by the results of the Jarque-Bera test (p 14 =.213; p 16 =.192; p 19 =.435), which was proven to outperform other tests of normality for sample sizes of around 100 (Frain, 2006). This enabled the use of parametric tests within further data analysis.
In order to ascertain whether each of the age groups exibits significant differences in understanding of the sublimation of water and the reaction of magnesium oxidation at 12a) write chemical equation of the reaction of magnesium oxidation: 12b) select the correct schematic representation of the mechanismo of the reaction of magnesium oxidation:

3)
12c) select the correct picture representation of the reaction of magnesium oxidation: the macroscopic, submicroscopic and symbolic level and whether the three age groups exhibit significant differences in the depth of understanding of the abovementioned concepts at each of the levels of chemistry knowledge, One-Way ANOVA was applied. The significance level for these analyses was .05. In instances where statistically significant differences had been found, Bonferroni's post hoc test was applied. The aim of these multiple pair-wise comparisons was to determine between which levels of chemistry knowledge (subitems within I1 and I2) the statistically significant differences in understanding occur for each age group, and between which age groups the statistically significant differences in the depth of understanding occur at each of the levels of chemistry knowledge. Conducting Bonferroni's correction presumed that for each of the pair-wise comparisons the significance level was kept at .05, while the p values were adjusted by multiplying the observed p value with the total number of comparisons that were carried out.

Results
Within I1, I1a referred to the sublimation of water at the symbolic level, I1b referred to this process at the macroscopic level, while I1c referred to the sublimation of water at the submicroscopic level. The proportion of correct answers (p) of the 14-year-old, 16-year-old and 19-year-old students to each of the subitems within I1 is presented in Table 1. The results of the comparison of achievements of the 14-year-old, 16-year-old and 19-year-old students on each of the subitems within I1 are presented in Table 2. Note. *Difference in the achievement is statistically significant at the level of p<.05.
The results presented in Table 2 indicate that there are statistically significant differences in the achievements of the three age groups of students on I1a, I1b and I1c. In order to determine between which age groups the statistically significant differences in the achievement occur on each of the subitems, pair-wise comparisons have been conducted. The results of these comparisons are presented in Table 3. Note. *Difference in the achievements of the two age groups is statistically significant at the level of p<.05.
As can be seen in Table 3, the 19-year-old students significantly outperformed the 14-year-old students on all of the subitems within I1. Furthermore, the 16-year-old students also significantly outperformed the 14-year-old students on I1a, I1b and I1c. At the same time, there were no statistically significant differences in the achievement of the 19-year-old and 16-year-old students, on any of the subitems within I1.
The results of the comparison of achievements of each age group of students on I1a, I1b and I1c are presented in Table 4. Note. *Difference in the achievements is statistically significant at the level of p<.05.
The results presented in Table 4 indicate that there are statistically significant differences in the achievements of each age group on the three subitems within I1. In order to determine between which subitems/levels of chemistry knowledge the statistically significant differences in achievements occur for each age group, pair-wise comparisons have been conducted. The results of these comparisons are presented in Table 5. Note. *Difference in the achievements on the two subitems is statistically significant at the level of p<.05.
As can be seen in Table 5, all three age groups of students showed significantly better understanding of the sublimation of water at the macroscopic (I1b), in comparison to the submicroscopic level (I1c). The results further indicate that all three age groups had significantly better understanding of the sublimation of water at the symbolic (I1a), in comparison to the submicroscopic level (I1c). On the other hand, none of the three age groups showed a significant difference in understanding of the sublimation of water at the macroscopic (I1b) and symbolic level (I1a).
Within I2, I2a referred to the reaction of magnesium oxidation at the symbolic level, I2b referred to this reaction at the submicroscopic level, while I2c referred to the reaction of magnesium oxidation at the macroscopic level. The proportion of correct answers (p) of the three age groups of students on each of the subitems within I2 is presented in Table 6. The results of the comparison of achievement of the 14-year-old, 16-year-old and 19-year-old students on each of the subitems within I2 are presented in Table 7. Note. *Difference in the achievement is statistically significant at the level of p<.05.
The results presented in Table 7 indicate that there are statistically significant differences in the achievements of the three age groups of students on I2a, I2b and I2c. In order to determine between which age groups the statistically significant differences in the achievements occur on each of the subitems, pair-wise comparisons have been conducted. The results of these comparisons are presented in Table 8. Note. *Difference in the achievements of the two age groups is statistically significant at the level of p<.05.
As can be seen in Table 8, the 19-year-old students significantly outperformed the 14-year-old students on all of the subitems within I2. Furthermore, the 16-year-old students also significantly outperformed the 14-year-old students on I2a, I2b and I2c. At the same time, there were no statistically significant differences in the achievements of the 19-year-old and 16-year-old students, on any of the subitems within I2.
The results of the comparison of achievements of each age group of students on I2a, I2b and I2c are presented in Table 9. Note. *Difference in the achievements is statistically significant at the level of p<.05.
The results presented in Table 9 indicate that there are statistically significant differences in the achievements of each age group on the three subitems within I2. In order to determine between which subitems/levels of chemistry knowledge the statistically significant differences in achievements occur for each age group, pair-wise comparisons have been conducted. The results of these comparisons are presented in Table 10. Note. *Difference in the achievements on the two subitems is statistically significant at the level of p<.05.
As can be seen in Table 10, all three age groups showed significantly better understanding of the reaction of magnesium oxidation at the macroscopic (I2c), in comparison to the submicroscopic level (I2b). The results further indicate that all three age groups had significantly better understanding of the reaction of magnesium oxidation at the symbolic (I2a), in comparison to the submicroscopic level (I2b). On the other hand, none of the three age groups showed a significant difference in the understanding of the reaction of magnesium oxidation at the macroscopic (I2c) and symbolic level (I2a).

Discussion and implications
The results of this study indicate that the 16-year-old and 19-year-old students have significantly better understanding of the sublimation of water and the reaction of magnesium oxidation at the macroscopic, submicroscopic and symbolic level, in comparison to the 14-year-old students. Such results are not contradictory to the assumption made within the model of the expanding triangle that students' understanding of chemical concepts, at all three levels of chemistry knowledge, increases with the age of students/number of years of Chemistry learning. However, no statistically significant differences in the understanding of the sublimation of water and the reaction of magnesium oxidation were found for the 16-year-old and 19-year-old students, at neither of the three levels of chemistry knowledge. This finding could, perhaps, be related to the 19-year-old students' ability to apply abstract thinking in regard to these particular concepts. More specifically, given their age, it is expected that all studens who formed the research sample reached the stage of formal operations in their cognitive development. This stage is marked by the development of abstract thinking, which enables students to understand abstract principles which have no physical reference, use symbols in order to represent and understand abstract concepts, and manipulate multiple variables simultaneously. Students are also able to make generalizations about the things that they have observed and use these concrete experiences in order to form hypotheses and consider concepts (Berk, 2007). Therefore, abstract thinking is a prerequisite for the development of conceptual understanding at all three levels of chemistry knowledge and dealing with all three levels simultaneously. It is important to note that the ability to think abstractly is greatly improved through practice. Furthermore, abstract thinking is domain specific, which is why practice of its application in one field of study will only promote abstract thinking in that particular domain (Slavin, 2006). After the reintroduction to the sublimation of water and the reaction of magnesium oxidation within the study of physical and chemical changes in the first year of grammar school (at the age of 16), the 19-year-old students also encountered these concepts in the second year of grammar school, within the study of inorganic chemistry. However, their next two years of Chemistry learning were devoted solely to the study of organic chemistry and biochemistry. Since under these conditions they had little opportunity to practice the application of abstract thinking in terms of physical and chemical changes of inorganic compounds, this could be the reason why they were not able to demonstrate significantly better understanding of the sublimation of water and the reaction of magnesium oxidation at each of the three levels of chemistry knowledge, in comparison to the 16-year-old students.
Research results further indicate that the 14-year-old, 16-year-old and 19-year-old students have significantly better understanding of the sublimation of water and the reaction of magnesium oxidation at the macroscopic and symbolic, in comparison to the submicroscopic level, while differences in understanding at the macroscopic and symbolic level are negligible. The results concerning the reaction of magnesium oxidation confirm the previous findings that students' understanding of chemical reactions tends to be limited to the macroscopic and symbolic level (Chandrasegaran et al., 2007;Jaber & BouJaoude, 2011) and that their ability to represent chemical reactions at the symbolic level is no guarantee of understanding at the submicroscopic level (Kern et al., 2010;Krajcik, 1991). The results concerning the understanding of the sublimation of water also confirm the previous finding that students tend to have better understanding of the process of sublimation at the macroscopic, in comparison to the submicroscopic level (Rahayu & Kita, 2010). In view of the fact that the 14-yearold, 16-year-old and 19-year-old students experienced the greatest difficulties with understanding of the sublimation of water and the reaction of magnesium oxidation at the submicroscopic level, it should be noted that teaching about physical and chemical changes at this level, to all three age groups, mostly revolved around static representations in Chemistry textbooks. On the other hand, Ardac and Akaygun (2005) found that students' understanding of these concepts at the particulate level could be improved through the use of dynamic computer representations. The abovementioned results also show that the 14-year-old students, who were just completing their first year of Chemistry learning, were able to deal with the sublimation of water and the reaction of magnesium oxidation at the macroscopic level more or at least as successfully as at the other two levels of chemistry knowledge. Therefore, the results of this study are not contrary to the assumption made within the rising iceberg model, that Chemistry teaching to novice students should start from the macroscopic level. However, they also imply that, when it comes to teaching these students about physical and chemical changes teachers could consider an early introduction of the symbolic level, alongside the macroscopic level. Introduction of another level, alongside the macroscopic level, has already been considered for teaching other branches of chemistry to novice students. For example, Johnstone (2000) recommended that introductory organic chemistry teaching should "begin with the macro and can afford to take in some submicro" (p.12). Given that the 16-year-old and 19-year-old students also showed significantly better understanding of the sublimation of water and the reaction of magnesium oxidation at the macroscopic and symbolic, in comparison to the submicroscopic level, research results further imply that each subsequent reintroduction of these concepts to older students should not differ from teaching to novice students, in terms of the sequence of levels in which the knowledge is presented.

Conclusion
This study explored how students' conceptual understanding of physical and chemical changes at the macroscopic, submicroscopic and symbolic level develops over time.
Within the study, 14-year-old, 16-year-old and 19-year-old students completed the test that checked their understanding of the sublimation of water as an example of a physical change and the reaction of magnesium oxidation as an example of a chemical change, at each of the levels. Thus obtained results were used in order to validate the previously proposed models of the expanding triangle and rising iceberg.
The study found that the 16-year-old and 19-year-old students have significantly better understanding of the sublimation of water and the reaction of magnesium oxidation in comparison to the 14-year-old students, at all three levels of chemistry knowledge. These findings support the proposition made within the expanding triangle model that students' understanding of chemistry concepts, at each of the three levels, increases with the age of students/number of years of chemistry learning. However, this study also found that, when it comes to the 16-year-old and 19-year-old students, differences in understanding of the abovementioned concepts at the macroscopic, submicroscopic and symbolic level are negligible. This could have been caused by the fact that the study dealt with physical and chemical changes of inorganic compounds, while the 19-year-old students, within their two previous years of Chemistry learning, dealt only with organic and biochemical compounds. Given that abstract thinking, which is a prerequisite for the development of conceptual understanding at all three levels of chemistry knowledge is domain specific, this could have impeded the development of the 19-year-old students' understanding of the sublimation of water and the reaction of magnesium oxidation at the macroscopic, submicroscopic and symbolic level. Therefore, it can be concluded that the way in which the Chemistry curriculum is composed has a profound impact on the development of students' conceptual understanding, at all three levels of chemistry knowledge.
The study also found that the 14-year-old, 16-year-old and 19-year old students have significantly better understanding of the sublimation of water and the reaction of magnesium oxidation at the macroscopic and symbolic, in comparison to the submicroscopic level, while differences in understanding at the macroscopic and symbolic level, for each age group, are negligible. Although such findings are not contrary to the assumption made within the rising iceberg model that Chemistry teaching to novice students should start from the macroscopic level, they do indicate that an early introduction of this content at the symbolic level, alongside the macroscopic level, could also be beneficial. Furthermore, each subsequent reintroduction of these concepts to older students should not differ from teaching them to novice students, in terms of the sequence of levels in which the knowledge is presented.
It is important to note that all research findings should be interpreted with caution, in view of certain limitations. First, the number of students from all three age groups is relatively small. Furthermore, the study was cross-sectional, whereas it might have been better if it had been longitudinal, so that only one population of students was followed over time. Therefore, within future research, the implementation of the longitudinal approach should be favored. Also, in order to draw general conclusions about the development of students' understanding of these concepts, more examples of physical and chemical changes should be considered. Finally, future research could examine whether the recommendations made within this study in regard to the teaching about physical and chemical changes have a positive impact on the development of students' understanding of these concepts, at all three levels of chemistry knowledge.